scholarly journals White Noise Tests on the LSTM Model Trained with Double Pendulum

2021 ◽  
Vol 2137 (1) ◽  
pp. 012032
Author(s):  
Xisen Wang
Keyword(s):  
Time Series ◽  
White Noise ◽  
Time Series Data ◽  
Initial Conditions ◽  
Correlation Coefficients ◽  
Series Data ◽  
Double Pendulum ◽  
Auto Correlation ◽  
State Dependent ◽  
Auto Regressive

Abstract This paper describes the intrinsic qualities of a simple double pendulum (DP), with a visual representation, a rigorous deduction of the Lagrangian equation, and a concrete factor analysis. LSTM model was utilized to simulate the double pendulum’s periodic and chaotic behaviors and evaluates the effectiveness of the model. The auto-correlation coefficients was calculated. Meanwhile, Box-Pierce test and Ljung-Box tests for various state-dependent time series were conducted to give various initial conditions to explore the DP system’s random characteristics. The research results are as follows: 1) Chaos did not lead to direct randomness; 2) seasonality could coexist with chaos; 3) the highly auto-regressive nature of DP’s time series data are found. Therefore, it can be concluded that the chaos in a double pendulum has particular patterns (such as the positive relationship with the likelihood of being a random white noise series) that could be further explored.

scholarly journals ESTIMATION OF AUTOREGRESSIVE ROOTS NEAR UNITY USING PANEL DATA

2000 ◽  
Vol 16 (6) ◽  
pp. 927-997 ◽  
Author(s):  
Hyungsik R. Moon ◽  
Peter C.B. Phillips
Keyword(s):  
Time Series ◽  
Panel Data ◽  
Time Series Data ◽  
Initial Conditions ◽  
Series Data ◽  
Test Statistics ◽  
Rate Condition ◽  
Panel Models ◽  
Stochastic Trends ◽  
Efficient Extraction

Time series data are often well modeled by using the device of an autoregressive root that is local to unity. Unfortunately, the localizing parameter (c) is not consistently estimable using existing time series econometric techniques and the lack of a consistent estimator complicates inference. This paper develops procedures for the estimation of a common localizing parameter using panel data. Pooling information across individuals in a panel aids the identification and estimation of the localizing parameter and leads to consistent estimation in simple panel models. However, in the important case of models with concomitant deterministic trends, it is shown that pooled panel estimators of the localizing parameter are asymptotically biased. Some techniques are developed to overcome this difficulty, and consistent estimators of c in the region c < 0 are developed for panel models with deterministic and stochastic trends. A limit distribution theory is also established, and test statistics are constructed for exploring interesting hypotheses, such as the equivalence of local to unity parameters across subgroups of the population. The methods are applied to the empirically important problem of the efficient extraction of deterministic trends. They are also shown to deliver consistent estimates of distancing parameters in nonstationary panel models where the initial conditions are in the distant past. In the development of the asymptotic theory this paper makes use of both sequential and joint limit approaches. An important limitation in the operation of the joint asymptotics that is sometimes needed in our development is the rate condition n/T → 0. So the results in the paper are likely to be most relevant in panels where T is large and n is moderately large.

scholarly journals Time series forecasting for the adobe software company’s stock prices using ARIMA (BOX-JENKIN’) model

2021 ◽  
Vol 2115 (1) ◽  
pp. 012044
Author(s):  
R. Vaibhava Lakshmi ◽  
S. Radha
Keyword(s):  
Time Series ◽  
Stock Prices ◽  
Time Series Data ◽  
Arima Model ◽  
Time Series Forecasting ◽  
Series Data ◽  
Auto Correlation ◽  
Correlation Plot ◽  
Best Fitting ◽  
Fitting Model

Abstract The time series forecasting strategy, Auto-Regressive Integrated Moving Average (ARIMA) model, is applied on the time series data consisting of Adobe stock prices, in order to forecast the future prices for a period of one year. ARIMA model is used due to its simple and flexible implementation for short term predictions of future stock prices. In order to achieve stationarity, the time series data requires second-order differencing. The comparison and parameterization of the ARIMA model has been done using auto-correlation plot, partial auto-correlation plot and auto.arima() function provided in R (which automatically finds the best fitting model based on the AIC and BIC values). The ARIMA (0, 2, 1) (0, 0, 2) [12] is chosen as the best fitting model, with a very less MAPE (Mean Absolute Percentage Error) of 3.854958%.

Revisiting the Holt-Winters' Additive Method for Better Forecasting

2019 ◽  
Vol 15 (2) ◽  
pp. 43-57
Author(s):  
Seng Hansun ◽  
Vincent Charles ◽  
Christiana Rini Indrati ◽  
Subanar
Keyword(s):  
Time Series ◽  
Average Method ◽  
Data Science ◽  
Time Series Data ◽  
Initial Conditions ◽  
Moving Average ◽  
Series Data ◽  
Initial Values ◽  
Additive Method ◽  
Weighted Moving Average

Time series are one of the most common data types encountered by data scientists and, in the context of today's exponentially increasing data, learning how to best model them to derive meaningful insights is an important skill in the Big Data and Data Science toolbox. As a result, many researchers have dedicated their efforts to developing time series analysis methods to predict future values based on previously observed values. One of the well-known methods is the Holt-Winters' seasonal method, which is commonly used to capture the seasonality effect in time series data. In this study, the authors aim to build upon the Holt-Winters' additive method by introducing new formulas for finding the initial values. Obtaining more accurate estimations of the initial values could result in a better forecasting result. The authors use the basic principle found in the weighted moving average method to assign more weight to the most recent data and combine it with the original initial conditions found in the Holt-Winters' additive method. Based on the experiment performed, the authors conclude that the new formulas for finding the initial values in the Holt-Winters' additive method could give a better forecasting when compared to the traditional Holt-Winters' additive method and the weighted moving average method in terms of the accuracy level.

Interpolated Mapping System Identification From Time Series Data

1993 ◽  
Author(s):  
Faruk H. Bursal ◽  
Benson H. Tongue
Keyword(s):  
Time Series ◽  
System Identification ◽  
Time Series Data ◽  
Initial Conditions ◽  
Series Data ◽  
Time Interval ◽  
Identification Algorithm ◽  
Regular Grid ◽  
Time Step ◽  
Data Set

Abstract In this paper, a system identification algorithm based on Interpolated Mapping (IM) that was introduced in a previous paper is generalized to the case of data stemming from arbitrary time series. The motivation for the new algorithm is the need to identify nonlinear dynamics in continuous time from discrete-time data. This approach has great generality and is applicable to problems arising in many areas of science and engineering. In the original formulation, a map defined on a regular grid in the state space of a dynamical system was assumed to be given. For the formulation to become practically viable, however, the requirement of initial conditions being taken from such a regular grid needs to be dropped. In particular, one would like to use time series data, where the time interval between samples is identified with the mapping time step T. This paper is concerned with the resulting complications. Various options for extending the formulation are examined, and a choice is made in favor of a pre-processing algorithm for estimating the FS map based on local fits to the data set. The suggested algorithm also has smoothing properties that are desirable from the standpoint of noise reduction.

scholarly journals Temporal Disaggregation Methods in Flow Variables of Economic Data: Comparison Study

2015 ◽  
Vol 5 (1) ◽  
pp. 36 ◽  
Author(s):  
Isaac O. Ajao ◽  
Femi J. Ayoola ◽  
Joseph O. Iyaniwura
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Mean Squared Error ◽  
Correlation Coefficients ◽  
Series Data ◽  
Absolute Difference ◽  
Temporal Disaggregation ◽  
Annual Time Series ◽  
Flow Variables ◽  
Accuracy Of Prediction

Annual Gross Domestic Product (GDP) for Nigeria using observed annual time-series data for the period 1981-2012 was studied. Five different econometric disaggregation techniques, namely the Denton, Denton-Cholette, Chow-Lin-maxlog, Fernandez, and Litterman-maxlog, are used for quarterisation. We made use of quarterly Export and Import as the indicator variables while disaggregating annual into quarterly data. The time series properties of estimated quarterly series were examined using various methods for measuring the accuracy of prediction such as, Theil's Inequality Coefficient, Root Mean Squared Error (RMSE), Absolute Mean Difference (MAD), and Correlation Coefficients. Results obtained showed that export and import are not good indicators for predicting GDP for Nigeria is concerned for the period covered. Denton method proved to be the worst using Mean Absolute Difference (MAD) and Theil’s Inequality Coefficient. However, RSME% and Pearson’s correlation coefficient gave robust values for Litterman-maxlog, thereby making it the best method of temporal disaggregation of Nigeria GDP.

scholarly journals PEMODELAN AUTOREGRESSIVE FRACTIONALLY INTEGRATED MOVING AVERAGE DENGAN EFEK EXPONENTIAL GARCH (ARFIMA-EGARCH) UNTUK PREDIKSI HARGA BERAS DI KOTA SEMARANG

2021 ◽  
Vol 10 (2) ◽  
pp. 279-292
Author(s):  
Rezky Dwi Hanifa ◽  
Mustafid Mustafid ◽  
Arief Rachman Hakim
Keyword(s):  
Time Series ◽  
Long Memory ◽  
Time Series Data ◽  
Moving Average ◽  
Financial Data ◽  
Series Data ◽  
Leverage Effect ◽  
Standard Equipment ◽  
Conditional Heteroscedasticity ◽  
Auto Regressive

Time series data is a type of data that is often used to estimate future values. Long memory phenomenon often occurs in time series data. Long memory is a condition that shows a strong correlation between observations even though they are quite far away. This phenomenon can be overcome by modeling time series data using the Autoregressive Fractional Integrated Moving Average (ARFIMA) model. This model is characterized by a fractional difference value. ARFIMA (Autoregressive Fractional Integrated Moving Average) model assumes that the residuals are normally distributed, mutually independent, and homogeneous. However, usually in financial data, the residual variants are not constant. This can be overcome by modeling variants. Standard equipment that can be used to model variants is the ARCH / GARCH (Auto Regressive Conditional Heteroscedasticity / Generalized Auto Regressive Conditional Heteroscedasticity) model. Another phenomenon that often occurs in GARCH models is the leverage effect on the residuals of the model. EGARCH (Exponential General Auto Regessive Conditional Heteroscedasticity) is a development of the GARCH model that is appropriate for data that has an leverage effect. The implementation of this model is by modeling financial data, so this study takes 136 monthly data on rice prices in Semarang City from January 2009 to April 2020. The purpose of this study is to create a long memory data forecasting model using the Exponential method. Generalized Autoregressive Conditional Heteroscedasticity (EGARCH). The best model obtained is ARFIMA (1, d, 1) EGARCH (1,1) which is capable of forecasting with a MAPE value of 3.37%.Keyword : Rice price, forecasting , long memory, leverage effect, GARCH, EGARCH

Modelling Monthly Volatility of the Muscat Securities Market (MSM) Index Using Auto Regressive Integrated Moving Average (ARIMA)

2019 ◽  
Vol 10 (11) ◽  
pp. 1045-1056
Author(s):  
Shaik Nafeez Umar Shaik ◽  
◽  
Labeeb Mohammed Zeeshan ◽  
Keyword(s):  
Time Series ◽  
Stock Market ◽  
Time Series Data ◽  
Moving Average ◽  
Performance Model ◽  
Securities Market ◽  
Series Data ◽  
Arima Models ◽  
Augmented Dickey Fuller ◽  
Auto Regressive

The Stock market is eyewitness’s responsive activities and is gradually more gaining importance. The purpose of the study is to measure the volatility of selected emerging indices Muscat Securities Market (MSM). Time series analysis techniques were used including Auto Regressive Integrated Moving Average (ARIMA) models. The time series data considered of this study taken MSM 30. The study period has taken from January 2013 to December 2018 except Sharia-compliant index would be June 2013 to December 2018. Tools used for the study is Unit Toot Test (Augmented Dickey–Fuller and Phillips-Perron), ARIMA models and for performance model using Theil’s U-Statistic. The study made a few observations which may help the investors and model builders to understand better about the stock market.

scholarly journals The Effect of High Positive Autocorrelation on the Performance of Garch Family Models

2018 ◽  
Author(s):  
Ngozi G. Emenogu ◽  
Monday Osagie Adenomon
Keyword(s):  
Time Series ◽  
Stock Prices ◽  
Time Series Data ◽  
Mean Squared Error ◽  
Financial Time Series ◽  
Absolute Error ◽  
Series Data ◽  
Asset Return ◽  
Financial Time ◽  
Auto Regressive

This study compared the performance of five Family Generalized Auto-Regressive Conditional Heteroscedastic (fGARCH) models (sGARCH, gjrGARCH, iGARCH, TGARCH and NGARCH) in the presence of high positive autocorrelation. To achieve this, financial time series was simulated with autocorrelated coefficients as &rho; = (0.8, 0.85, 0.9, 0.95, 0.99), at different time series lengths (as 250, 500, 750, 1000, 1250, 1500) and each trial was repeated 1000 times carried out in R environment using rugarch package. And the performance of the preferred model was judged using Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE). Results from the simulation revealed that these GARCH models performances varies with the different autocorrelation values and at different time series lengths. But in the overall, NGARCH model dominates with 62.5% and 59.3% using RMSE and MAE respectively. We therefore recommended that investors, financial analysts and researchers interested in stock prices and asset return should adapt NGARCH model when there is high positive autocorrelation in the financial time series data.

scholarly journals Application of ARIMA Model for River Discharges Analysis

2017 ◽  
Vol 4 (1) ◽  
pp. 27 ◽  
Author(s):  
Bhola NS Ghimire
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Moving Average ◽  
Arima Model ◽  
Series Data ◽  
Hydrological Data ◽  
Time Component ◽  
Data Points ◽  
Auto Regressive ◽  
Component Time

<p class="Default">Time series data often arise when monitoring hydrological processes. Most of the hydrological data are time related and directly or indirectly their analysis related with time component. Time series analysis accounts for the fact that data points taken over time may have an internal structure (such as autocorrelation, trend or seasonal variation) that should be accounted for. Many methods and approaches for formulating time series forecasting models are available in literature. This study will give a brief overview of auto-regressive integrated moving average (ARIMA) process and its application to forecast the river discharges for a river. The developed ARIMA model is tested successfully for two hydrological stations for a river in US.</p><p><strong>Journal of Nepal Physical Society</strong><em><br /></em>Volume 4, Issue 1, February 2017, Page: 27-32</p>

Sign in / Sign up

Export Citation Format

Share Document